7(2x^2+4x+6)-6(3x^2+3x+7)=

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Solution for 7(2x^2+4x+6)-6(3x^2+3x+7)= equation: 


Simplifying
7(2x2 + 4x + 6) + -6(3x2 + 3x + 7) = 0

Reorder the terms:
7(6 + 4x + 2x2) + -6(3x2 + 3x + 7) = 0
(6 * 7 + 4x * 7 + 2x2 * 7) + -6(3x2 + 3x + 7) = 0
(42 + 28x + 14x2) + -6(3x2 + 3x + 7) = 0

Reorder the terms:
42 + 28x + 14x2 + -6(7 + 3x + 3x2) = 0
42 + 28x + 14x2 + (7 * -6 + 3x * -6 + 3x2 * -6) = 0
42 + 28x + 14x2 + (-42 + -18x + -18x2) = 0

Reorder the terms:
42 + -42 + 28x + -18x + 14x2 + -18x2 = 0

Combine like terms: 42 + -42 = 0
0 + 28x + -18x + 14x2 + -18x2 = 0
28x + -18x + 14x2 + -18x2 = 0

Combine like terms: 28x + -18x = 10x
10x + 14x2 + -18x2 = 0

Combine like terms: 14x2 + -18x2 = -4x2
10x + -4x2 = 0

Solving
10x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(5 + -2x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {0, 2.5}

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